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Similar Figures/Transcript
Transcript Title text reads, The Mysteries of Life with Tim and Moby Tim and Moby are playing with action figures in the backyard. Tim holds up a superhero figure. TIM: [in Agent Awesome superhero voice] You'll never make it, Captain Evil! Moby pushes a super-villain figure on a motorcycle up a wooden ramp. The figure soars over a fish tank, but not high enough. It falls into the water. TIM: Told ya you wouldn't make it. A letter appears. Text reads as Tim narrates: Dear Tim and Moby, can you help me on using similar figures? Thanks, Chase Dixon. TIM: Sure thing, Chase! In everyday conversation, the word, similar, is just another way of describing things that are alike. But in math, it has a more specific meaning. Figures are geometrically similar if they have the same shape, but not necessarily the same size. A label appears, reading, geometrically similar. Moby beeps. TIM: Nope, it doesn't mean that all triangles are similar; triangles can have very different shapes! Take the triangle on Captain Evil's chest… his Triangle of Evil! On-screen, the triangle on the Captain Evil figure's chest glows. Moby rolls his eyes and beeps. TIM: Sorry. Okay, as you can see, it's an equilateral triangle, which means it has three sides of equal length and three 60-degree angles. A label appears, reading, equilateral. An equilateral triangle appears. Each side is labeled, 2 centimeters. Each angle is labeled, 60 degrees. TIM: So now check out this wooden block, which is also triangular. On-screen, the wooden ramp appears. TIM: This is a scalene triangle, with sides of different lengths and three different angles. A label appears, reading, scalene. The wooden ramp becomes a scalene triangle. The sides are labeled, 6, 8, and 10 centimeters. The angles are labeled, 37, 53 and 90 degrees. TIM: Geometrically similar triangles have to have corresponding angles that are congruent, or equal. These don’t. A label appears, reading, congruent. A not equal sign appears between the equilateral triangle and the scalene triangle. TIM: And they would have to have corresponding sides that are all proportional in length. And that means that the relative lengths of the sides would have to be the same. A label appears, reading, proportional. TIM: Our equilateral triangle has sides of lengths 2 centimeters, 2 centimeters, and 2 centimeters. Since they’re all the same, we can reduce that ratio to 1 to 1 to 1. A ratio appears, reading, 2 to 2 to 2. It becomes the ratio, 1 to 1 to 1. TIM: The scalene triangle has sides of 6 centimeters, 8 centimeters, and 10 centimeters. We can reduce those numbers by dividing by 2 to make the relative sizes 3, 4, and 5. A ratio appears, reading, 3 to 4 to 5. TIM: The sides are obviously not in the same proportion; and the angles are all different. So these triangles are not similar. Moby beeps. TIM: Good idea! Let’s compare Captain Evil's triangle with the triangle formed by the ground and our swing set’s legs. On-screen, a swing set appears. Two legs form a triangle with the ground. TIM: The angles of this big triangle are all 60 degrees, just like the Triangle of Evil! On-screen, each angle is labeled, 60 degrees. Each side is labeled, 4 meters. TIM: And since the sides are all the same length, they form the same ratio with the corresponding sides of the smaller triangle. So they're officially similar! A ratio appears, reading, 4 to 4 to 4. Another ratio appears, reading, 2 to 2 to 2. An equal sign appears between the ratios. Moby beeps. TIM: Right, even though the swing set triangle is much bigger than the Triangle of Evil, the corresponding sides have the same proportions. If we wanna find out the size difference between the two triangles, we can use something called scale factor. A label appears, reading, scale factor. TIM: To find the scale factor between two similar geometric shapes, you just simplify the ratio between any two corresponding measurements; not including angles. Let's use two sides from our triangles. The ratio is 4 meters to 2 centimeters. A ratio appears, reading, 4 meters to 2 centimeters. It becomes the ratio, 400 centimeters to 2 centimeters, and then the ratio, 200 centimeters to 1 centimeter. TIM: The big triangle is 200 times bigger than the small one! By the way, this applies to all kinds of shapes, not just triangles. Moby beeps. TIM: Well, all squares are similar by definition, since they all have four equal sides and four 90-degree angles. A square appears. Each side is the same length. Each angle is labeled, 90 degrees. TIM: The same goes with circles; you can read more about that in our features! But other shapes you do have to measure out. Moby beeps. TIM: Sure, there's plenty of things you can do with similar figures. One is called indirect measurement. A label appears, reading, indirect measurement. TIM: That's a way to measure things that are way too big to measure directly; like how tall that tree is! See how the tree casts a shadow to make a triangle? On-screen, a tree casts a shadow on the ground. A dotted line connects the top of the tree to the end of the shadow. TIM: Well, we can use a meter stick to create a similar shadow and triangle. Moby holds a meter stick perpendicular to the ground. It casts a shadow. A dotted line connects the top of the stick to the end of the shadow, forming a triangle. TIM: We already know the length of the meter stick, 1 meter, and we can measure the length of both shadow lines on the ground. On-screen, the height of the tree is labeled, x. The shadow of the tree is labeled, 4.8 meters. The height of the stick is labeled, 1 meter. The shadow of the stick is labeled, 0.6 meters. TIM: Now we make a ratio for the lengths we know and solve for x! An equation appears, reading, x, over 4.8 equals 1 over 0.6. The equation becomes, x, equals 4.8 over 0.6, equals 8. TIM: The tree's 8 meters tall! [in superhero voice] Which is exactly how far Agent Awesome can toss your puny Captain Evil if he’s dumb enough to… On-screen, Moby grabs the Agent Awesome figure out of Tim's hand. TIM: Hey! Moby beeps. He throws the figure over the fence into the next yard. Category:BrainPOP Transcripts Category:BrainPOP Math Transcripts